Interferometric optical techniques are widely used to characterize test surfaces.
For example, to measure the surface profile of a test surface, one can use an interferometer to combine a test wavefront reflected from the test surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined test and reference wavefronts caused by variations in the profile of the test surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the test surface. The surface profile measurement of the test surface is relative to the surface profile of the reference surface, which is assumed to be perfect (e.g., flat) or known within the tolerances of the measurement.
With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and test wavefronts to produce a series of optical interference patterns that span, for example, at least a half cycle of optical interference (e.g., from constructive, to destructive interference). The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase-offset equal to the phase difference between the combined test and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase-offset for each spatial location is extracted from the sinusoidal dependence of the intensity values to provide a profile of the test surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
The phase-shifts in PSI can be produced by changing the optical path length from the measurement surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved relative to the measurement surface. Alternatively, the phase-shifts can be introduced for a constant, non-zero optical path difference by changing the wavelength of the measurement and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren.
One type of interferometer that is often used for characterizing a surface of a test object is a Fizeau interferometer. In many embodiments, phase shifting for object surface profiling proceeds by mechanical translation of the reference surface or by wavelength tuning, during which time a computer captures successive frames of an interference pattern at a detector for later analysis.
In certain cases, it is useful to operate an interferometer using single-frame data acquisition with short integration times, where environmental disturbances such as vibration and air turbulence are minimized and the acquisition of dynamically-changing events may be realized. In one embodiment, the requirement of multiple phase shifts across a single camera frame is accomplished by the introduction of dense carrier fringes. However, operating interferometers in a way to spatially encode the phase shifts required for single-frame data acquisition can, in some instances, introduce other errors known as “retrace errors.” A retrace error occurs in a Fizeau-type interferometer, for example, when two interfering beams (e.g., a measurement beam and reference beam) depart from a common imaging path and, as a result, accumulate additional and differing phase contributions due to system design or spatially local imperfections in the traversed optical components. That is, a retrace error refers to a systematic error (e.g., accumulated phase difference).